Weak geodesic flow and global solutions of the Hunter-Saxton equation
Jonatan Lenells
We show how global weak solutions of the Hunter-Saxton equation can be naturally constructed using the geometric interpretation of the equation as the Euler equation for the geodesic flow on an $L^2$-sphere. The approach involves forming a weak extension of the geodesic flow and relating it to a corresponding weak formulation of the Hunter-Saxton equation.
keywords: Hunter-Saxton equation Weak geodesic flow Global weak solutions.
Traveling waves in compressible elastic rods
Jonatan Lenells
We determine all weak traveling wave solutions of a model for nonlinear dispersive waves in cylindrical compressible hyperelastic rods. Besides the previously known smooth, peaked, and cusped solutions, the equation is shown to admit compactons, stumpons, and fractal-like waves.
keywords: Traveling waves Nonlinear wave equations. Elasticity

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